Question: Solve for $x$ and $y$ using substitution. ${-2x+6y = -10}$ ${y = -5x-7}$
Since $y$ has already been solved for, substitute $-5x-7$ for $y$ in the first equation. ${-2x + 6}{(-5x-7)}{= -10}$ Simplify and solve for $x$ $-2x-30x - 42 = -10$ $-32x-42 = -10$ $-32x-42{+42} = -10{+42}$ $-32x = 32$ $\dfrac{-32x}{{-32}} = \dfrac{32}{{-32}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = -5x-7}\thinspace$ to find $y$ ${y = -5}{(-1)}{ - 7}$ $y = 5 - 7$ $y = -2$ You can also plug ${x = -1}$ into $\thinspace {-2x+6y = -10}\thinspace$ and get the same answer for $y$ : ${-2}{(-1)}{ + 6y = -10}$ ${y = -2}$